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{excerpt:hidden=true}*System:* Any system can be treated as a [point particle] located at the [center of mass]. --- *Interactions:* Any.{excerpt}

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h1. Point Particle Dynamics

h4. {toggle-cloak:id=desc} Description and Assumptions

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This [model|model] is applicable to a [point particle] (or to a [system|system] of objects treated as a [point particle|point particle] located at the system's [center of mass]) when the [external forces|external force] are known or needed.  It is a subclass of the model [Momentum and External Force] defined by the constraint _dm/dt_ = 0.
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h4. {toggle-cloak:id=cues} Problem Cues

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This [model|model] is typically applied to find the [acceleration|acceleration] in cases where the [forces|force] will remain constant, such as an object moving along a flat surface like a ramp or a wall.  It is also useful in combination with other [models|model], such as when finding the [normal force|normal force] exerted on a passenger in a roller coaster at the top of a loop-the-loop (in which case, it would be combined with [Mechanical Energy and Non-Conservative Work]).
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h4. {toggle-cloak:id=pri} Prior Models

{cloak:id=pri}Learning Objectives

Students will be assumed to understand this model who can:

* State [One-Dimensional Motion with Constant Acceleration|1-D Motion (Constant Acceleration)].

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h4. {toggle-cloak:id=vocab} Vocabulary

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h2and explain the significance of Newton's Laws of Motion.
* Define [normal force] and describe its relationship to [weight].
* Discriminate between [static|static friction] and [kinetic|kinetic friction] friction.
* Explain the role of the [coefficient of friction] in both the [kinetic|kinetic friction] and [static|static friction] cases.
* Construct a [free body diagram] for an object subject to [contact forces|contact force], [gravity|gravity (near-earth)], [elastic forces|Hooke's Law for elastic interactions], and/or [tension forces|tension].  
* Construct and solve a system of equations describing the dynamics of more than one object that interact with one another.


h1. Model

h4. {toggle-cloak:id=sys} {color:red}Compatible Systems{color}

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A single [point particle|point particle], or a system of constant mass that is treated as a point particle located at the system's center of mass.
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h4. {toggle-cloak:id=int} {color:red}Relevant Interactions{color}
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[External forces|external force] must be understood sufficiently to draw a [free body diagram] for the system.  [Internal forces|internal force] will always cancel from the equations of Newton's 2nd Law for the system and can be neglected.
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h4. {toggle-cloak:id=law} {color:red}Law of Change{color}

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{latex}\begin{large} \[ \sum \vec{F}^{\rm ext} = m\vec{a} \]  \end{large} {latex}

{note}As with all vector equations, this Law of Interaction should really be understood as three simultaneous equations:\\

{latex}\begin{large}\[ \sum F^{\rm ext}_{x} = ma_{x}\]
\[ \sum F^{\rm ext}_{y} = ma_{y}\]
\[\sum F^{\rm ext}_{z} = ma_{z}\]\end{large}{latex}{note}
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h4. {toggle-cloak:id=diag} {color:red}Diagrammatical Representations{color}

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h2

* [Free Body Diagram|free body diagram]

h1. Relevant Examples

h4. {toggle-cloak:id=vec} Examples Involving Vector Components
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h4. {toggle-cloak:id=norm} Examples Involving Normal Force
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h4. {toggle-cloak:id=appw} Examples Involving Apparent Weight
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h4. {toggle-cloak:id=tens} Examples Involving Tension
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h4. {toggle-cloak:id=incl} Examples Involving Inclined Planes
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h4. {toggle-cloak:id=stat} Examples Involving Static Friction
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h4. {toggle-cloak:id=kin} Examples Involving Kinetic Friction
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h4. {toggle-cloak:id=cen} Examples Involving Centripetal Acceleration
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h4. {toggle-cloak:id=all} All Examples Using this Model
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Photos courtesy:
[US Navy|http://www.navy.mil] by Mass Communication Specialist 3rd Class James R. Evans

[US Army|http://www.army.mil] by Spc. Michelle Waters


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